Simulate and plot a random function \(\eta(\cdot)\) on \((0,2 \pi)\) whose covariance is \(\pi / 2-\ell\left(t, t^{\prime}ight)\), where \(\ell(\cdot)\) is the arc-length metric. This function is less well behaved than the chordal function because half of its Fourier coefficients are zero, so the simulation code must be modified to accommodate singularities.